Occupation Measures of Singularly Perturbed Markov Chains with Absorbing States

Abstract This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states. It focuses on both unscaled and scaled occupation measures. Under mild conditions, a mean-square estimate is obtained. By averaging the fast components, we obtain an aggregated process. Although the aggregated process itself may be non-Markovian, its weak limit is a Markov chain with much smaller state space. Moreover, a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component. * The research of this author is supported in part by the National Science Foundation under Grant DMS-9877090 ** The research of this author is supported in part by the Office of Naval Research Grant N00014-96-1-0263 *** The research of this author is supported in part by Wayne State University